This paper studies the generalized synchronization of a class of drive-response neural networks with time-varying delay. When the topological structures of the drive-response neural networks are known, by designing an appropriate nonlinear adaptive controller, the generalized synchronization of these two networks is obtained based on Lyapunov stability theory and LaSalle’s invariance principle.
Watts, D. and Strogatz, S. (1998) Collective Dynamics of “Small-World” Networks. Nature, 393, 440-442. https://doi.org/10.1038/30918
Ott, E. (2002) Chaos in Dynamical Systems. Cambridge Univ. Press, Cambridge. https://doi.org/10.1017/CBO9780511803260
Watts, M. (1999) Renormalization Group Analysis of the Small-World Network Model. Physics Letters A, 263, 341-346. https://doi.org/10.1016/S0375-9601(99)00757-4
Newman, M. and Watts, D.J. (1999) Scaling and Percolation in the Small-World Network Model. Physical Review E, 60, 7332-7342. https://doi.org/10.1103/PhysRevE.60.7332
Benson, A., Gleich, R.D.F. and Leskovec, J. (2016) Higher-Order Organization of Complex Networks. Science, 353, 163-166. https://doi.org/10.1126/science.aad9029
Guo, W. (2011) Lag Synchronization of Complex Networks via Pinning Control. Nonlinear Analysis Real World Applications, 12, 2579-2585. https://doi.org/10.1016/j.nonrwa.2011.03.007
Yu, C.B., Qin, J. and Gao, H. (2014) Cluster Synchronization in Directed Networks of Partial-State Coupled Linear Systems under Pinning Control. Automatica, 50, 2341-2349. https://doi.org/10.1016/j.automatica.2014.07.013
Chung, S.J., Bandyopadhyay, S., Chang, I. and Hadaegh, F.Y. (2013) Phase Synchronization Control of Complex Networks of Lagrangian Systems on Adaptive Digraphs. Automatica, 49, 1148-1161. https://doi.org/10.1016/j.automatica.2013.01.048
Wang, J.A. and Liu, H.P. (2010) Adaptive Synchronization between Two Different Complex Networks with Time-Varying Delay Coupling. Journal of University of Science and Technology Beijing, 32, 61-64.
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y. and Zhou, C. (2008) Synchronization in Complex Networks. Physics Reports, 18, Article ID: 037111.
Radenković, M.S. and Krstić, M. (2018) Distributed Adaptive Consensus and Synchronization in Complex Networks of Dynamical Systems. Automatica, 91, 233-243. https://doi.org/10.1016/j.automatica.2018.01.039
Yang, L.X. and Jiang, J. (2014) Adaptive Synchronization of Drive-Response Fractional-Order Complex Dynamical Networks with Uncertain Parameters. Communications in Nonlinear Science & Numerical Simulation, 19, 1496-1506. https://doi.org/10.1016/j.cnsns.2013.09.021
Chen, X. and Lu, J. (2007) Adaptive Synchronization of Different Chaotic Systems with Fully Unknown Parameters. Physics Letters A, 364, 123-128. https://doi.org/10.1016/j.physleta.2006.11.092
Yang, X., Cao, J. and Lu, J. (2012) Stochastic Synchronization of Complex Networks with Nonidentical Nodes via Hybrid Adaptive and Impulsive Control. IEEE Transactions on Circuits and Systems I Regular Papers, 59, 371-384. https://doi.org/10.1109/TCSI.2011.2163969
Han, X., Lu, J.A. and Wu, X. (2008) Synchronization of Impulsively Coupled Systems. International Journal of Bifurcation and Chaos, 18, 1539-1549. https://doi.org/10.1142/S0218127408021154
Qiang, S. and Cao, J. (2010) On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks. Circuits and Systems I: Regular Papers, IEEE Transactions on Circuits and Systems I Regular Papers, 57, 672-680. https://doi.org/10.1109/TCSI.2009.2024971
Deng, L., Wu, Z. and Wu, Q. (2013) Pinning Synchronization of Complex Network with Non-Derivative and Derivative Coupling. Nonlinear Dynamics, 73, 775-782. https://doi.org/10.1007/s11071-013-0830-y
Razminia, A. and Baleanu, D. (2013) Complete Synchronization of Commensurate Fractional Order Chaotic Systems Using Sliding Mode Control. Mechatronics, 23, 873-879. https://doi.org/10.1016/j.mechatronics.2013.02.004
Hu, M., Yang, Y., Xu, Z., Rong, Z. and Guo, L. (2007) Projective Synchronization in Drive-Response Dynamical Networks. Physica A: Statistical Mechanics and Its Applications, 381, 457-466. https://doi.org/10.1016/j.physa.2007.03.023
Mei, S., Zeng, C.Y. and Tian, L.X. (2008) Projective Synchronization in Drive-Response Dynamical Networks of Partially Linear Systems with Time-Varying Coupling Delay. Physics Letters A, 372, 6904-6908. https://doi.org/10.1016/j.physleta.2008.10.019
Shang, Y., Chen, M. and Kurths, J. (2009) Generalized Synchronization of Complex Networks. Physical Review E Statistical Nonlinear and Soft Matter Physics, 80, Article ID: 027201. https://doi.org/10.1103/PhysRevE.80.027201
Wu, X., Wei, X.Z. and Jin, Z. (2009) Generalized Outer Synchronization between Complex Dynamical Networks. Chaos, 19, Article ID: 013109. https://doi.org/10.1063/1.3072787
Wang, J.A. (2012) Adaptive Generalized Synchronization between Two Different Complex Networks with Time-Varying Delay Coupling. Acta Physica Sinica, 61, Article ID: 020509. https://doi.org/10.7498/aps.61.020509
Cao, J.D., Li, P. and Wang, W.W. (2006) Global Synchronization in Arrays of Delayed Neural Networks with Constant and Delayed Coupling. Physics Letters A, 353, 318-325. https://doi.org/10.1016/j.physleta.2005.12.092
Langville, A.N. and Stewart, W.J. (2004) The Kronecker Product and Stochastic Automata Networks. Journal of Computational and Applied Mathematics, 167, 429-447. https://doi.org/10.1016/j.cam.2003.10.010
Liu, H., Lu, J.A. and Lu, J.H. (2009) Structure Identification of Uncertain General Complex Dynamical Networks with Time Delay. Automatica, 45, 1799-1807. https://doi.org/10.1016/j.automatica.2009.03.022
Aeyels, D. (1995) Asymptotic Stability of Nonautonomous Systems by Lyapunov’s Direct Method. Systems and Control Letters, 25, 273-280. https://doi.org/10.1016/0167-6911(94)00088-D